Perform the indicated operation. Simplify if possible.
$\frac{8}{x + 7} - \frac{7 x}{x^{2} - 49}$
$\frac{8}{x + 7} - \frac{7 x}{x^{2} - 49} = ◻ ($ Simplify your answer.)

Answer

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Answer

Final Answer: $\frac{x - 56}{x^{2} - 49}$

Steps

Step 1 ：Find a common denominator for the two fractions, which is $(x + 7) (x - 7)$

Step 2 ：Rewrite both fractions with the common denominator: $\frac{8}{x + 7} \cdot \frac{x - 7}{x - 7} - \frac{7 x}{x^{2} - 49}$

Step 3 ：Simplify the expression: $\frac{8 (x - 7)}{(x + 7) (x - 7)} - \frac{7 x}{(x + 7) (x - 7)}$

Step 4 ：Combine the fractions: $\frac{8 (x - 7) - 7 x}{(x + 7) (x - 7)}$

Step 5 ：Simplify the numerator: $\frac{8 x - 56 - 7 x}{(x + 7) (x - 7)}$

Step 6 ：Combine like terms: $\frac{x - 56}{(x + 7) (x - 7)}$

Step 7 ：Final Answer: $\frac{x - 56}{x^{2} - 49}$